FUNDAMENTALS OF MODIFIED RELEASE FORMULATIONS Dr. Basavraj K. Nanjwade M. Pharm., Ph. D Professor of Pharmaceutics Department of Pharmaceutics KLE University College of Pharmacy BELGAUM – 590010, Karnataka, INDIA 1 CONTENTS: Diffusion controlled Dissolution controlled Erosion controlled and hybrid system in drug delivery Mathematical models Design and optimization of release rates based desired pharmacokinetic profile 2 DIFFUSION CONTROLLED In these type of system the rate controlling step is not dissolution rate but the diffusion of dissolved drug through a polymeric barrier. Since the diffusional path length increases with time as the insoluble matrix is gradually depleted by the drug and the release of drug is never zero order. This system are broadly classified into two categories reservoir system and monolithic system. 3 DIFFUSION CONTROLLED There are following type of diffusion controlled system 1. Reservoir devices 2. Matrix devices 1. Reservoir devices: Drug will partition in to the membrane and exchange with fluid surrounding the particle or tablet. The water soluble polymer material encases a core of drug. Additional drug will enter the membrane, diffuse to the periphery and exchange with the surrounding media. 4 RESERVOIR DIFFUSION CONTROLLED SYSTEM These systems are hollow in which core of drug is surrounded in water insoluble polymer membrane. Coating or microencapsulation technique are used to apply polymer. The permeability of membrane depend on thickness of the coat/concentration of coating solution & on the nature of polymer, ethyl cellulose and polyvinyl acetate are the commonly used polymer in such devices. 5 RESERVOIR DIFFUSION CONTROLLED SYSTEM The mechanism of drug release across the membrane involves partitioning into the membrane with subsequent release into the surrounding fluid by diffusion. The rate of drug release from the reservoir system can be explained by Fick ’s Law of diffusion as per the following equation. dm/dt = DSK(ΔC)/l 6 dm/dt = DSK(ΔC)/l Where, S = is the active diffusion area. D = is the diffusion coefficient of the drug across the coating membrane. l = is the diffusional path length (thickness of polymer coat) ΔC = is the concentration difference across l. K = is the partition coefficient of the drug between polymer and the external medium. 7 METHODS TO DEVELOP THE RESERVOIR DEVICES There are 2 processes used to apply insoluble polymeric materials to enclose drug containing core in tablets. Press coating & Air suspension techniques Microencapsulation process is commonly used. In most cases drug is incorporated in coating film as well as in the microcapsule. Care should be taken during placement into tablet or capsule dosage forms to minimize fragmentation or fusion of the particle both effects will alter release characteristics. 8 2. MATRIX DIFFUSION CONTROLLED SYSTEM In these system the drug is dispersed in insoluble matrix of rigid non swellable hydrophobic materials or swellable hydrophilic substances. Insoluble plastics such as PVC and fatty materials like stearic acid, beeswax etc are the material used for rigid matrix. The drug is generally kneaded within the solution of plastic material such as PVC in an organic solvent and granulated. The wax drug matrix is prepared by dispersing the drug in molten fat followed by congealing. 9 MATRIX DIFFUSION CONTROLLED SYSTEM 10 MATRIX DIFFUSION CONTROLLED SYSTEM • The equation describing drug release for this system is given by T. Higuchi. Q=[Dἐ /T (La-ἐCs)Cs t]1/2 Q = weight in gram of drug release/unit surface area D = diffusion coefficient Cs = solubility of drug in the release medium ἐ = Porosity of matrix T = tourtuosity of matrix A = Concentration of drug in the tablet express as g/ml 11 MATRIX DIFFUSION CONTROLLED SYSTEM Assumptions made in the previous equations : A pseudo-steady state is maintained during release . A>>Cs , i.e. , excess solute is present . C=0 in solution at all times ( perfect sink ) . Drug particles are much smaller than those in the matrix . The diffusion coefficient remains constant . No interaction between the drug and the matrix occurs . 12 MATRIX DIFFUSION CONTROLLED SYSTEM The release of highly water soluble drug can be sustained by using swellable matrix systems. Hydrophilic gums may be of natural origin (Guar gum, tragacanth), semi synthetic (HPMC, CMC, Xanthan gum) or synthetic (poly acryl amides) are the material generally used for such matrices. In the solvent such as alcohol the gum and drug are granulated together and compressed into tablet. 13 MATRIX DIFFUSION CONTROLLED SYSTEM The mechanism of drug release from this system involves initial dehydration of hydrogel followed by absorption of water and desorption of drug via swelling controlled diffusion mechanism. As the gum swells and the drug diffuses out of it, the swollen mass devoid of drug appear transparent or glass like and so the system is sometimes called as glassy hydrogel. 14 Advantages and Disadvantages of Matrix and Reservoir system Matrix system Suitable for both nondegradable and degradable system. No danger of ‘dose dumping’ in case of rupture. Achievement of ‘zero order’ release is difficult. Reservoir system Degradable reservoir systems may be difficult to design Rupture can result in dangerous Dose dumping. Achievement of zero order release is easy. 15 DISSOLUTION CONTROLLED RELEASE These system are easiest to design. The drug with slow dissolution rate is inherently sustained. E.g. Griseofulvin, Digoxin and Saliyclamide & they act as natural prolonged release products. 16 DISSOLUTION CONTROLLED RELEASE Aluminum aspirin and ferrous sulfate produce slow dissolving form when it comes in contact with GI fluids. Drugs having high aqueous solubility & dissolution rate E.g. Pentoxifylline steroid undergo transformation into less soluble polymorphs during dissolution in absorption pool. 17 DISSOLUTION CONTROLLED RELEASE The basic principle of dissolution control is as follows: If the dissolution process is diffusion layer controlled where the rate of diffusion from the solid surface through a unstirred liquid film to the bulk solution is rate limiting, the flux ‘J’ is given by J= -D(dc/dx) Where, D = Diffusion coefficient. Dc/ dx = Concentration gradient between the solid surface and bulk of solution. 18 DISSOLUTION CONTROLLED RELEASE In terms of flow rate of material (dm/dt) through unit area (A), the flux can be given as J = (1/A) dm/dt For the system with linear concentration gradient and thickness of the diffusion layer ‘h’ dc/ dx = (Cb - Cs) Where Cs represents the concentration at the solid surface and Cb is the bulk solution concentration. A combined equation for rate of material is given as dm/dt = - (DA/h) (Cb - Cs) = kA (Cs - Cb) Where, k is intrinsic dissolution rate constant. 19 Dissolution controlled release products are divided in two classes: 1) Encapsulation dissolution control. 2) Matrix dissolution control. 1. Encapsulation/Coating dissolution controlled system (Reservoir Devices): Encapsulation involves coating of individual particles, or granules of drug with the slowly dissolving material. The particles obtained after coating can be compressed directly into tablets as in spacetabs or placed in capsules as in the spansule products. 20 Encapsulation/Coating dissolution controlled system (Reservoir Devices): As the time required for dissolution of coat is a function of its thickness and the aqueous solubility of the polymer one can obtain the coated particles of varying thickness in the range of 1- 200 micron. 21 Encapsulation/Coating dissolution controlled system (Reservoir Devices): By using one of several microencapsulation techniques the drug particles are coated or encapsulated with slowly dissolving materials like cellulose, PEGs, olymethacrylates, waxes etc. Two methods of preparation are employed : 1. Seed or granule coating 2. Microencapsulation 22 Encapsulation/Coating dissolution controlled system (Reservoir Devices): Seed or Granule Coated Products : Procedure: Non pareil seeds are coated with drug This followed with by a coat of slowly dissolving material such as carbohydrate sugars & cellulose , PEG , polymeric material & wax. Coated granules can be placed in a capsule for administration. E.g. amobarbital & dextroamphetamine sulfate Microencapsulation : • This method can be used to encase liquids , solids , or gases. E.g. aspirin & potassium chloride • Advantage of this method is that sustained drug release can be achieved with taste abatement & better GI tolerability. 23 MICROENCAPSULATION PROCESSES PROCESSES TYPES OF MATERIALS FOR COATING COASERVATION/ PHASE SEPARATION WATER –SOLUBLE POLYMER INTERFACIAL POLYMERIZATION WATER-INSOLUBLE &WATER SOLUBLE MONOMER ELECTOSTATIC METHOD PRECIPITATION HOT MELT SALTING OUT SOLVENT EVAPORATION OPPOSITELY CHARGED AEROSOLS WATER OR SOLVENT-SOLUBLE POLYMER LOW MOLECULAR WEIGHT LIPIDS WATER-SOLUBLE POLYMERS SOLVENT-SOLUBLE POLYMERS 24 2. Matrix (or Monolith)/ Embedded dissolution controlled system. Since the drug is homogeneously dispersed throughout a rate controlling medium matrix system are also called monoliths. The waxes used for such system are beeswax, carnauba wax, hydrogenated castor oil etc. These waxes control the drug dissolution by controlling the rate of dissolution fluid penetration into the matrix by altering the porosity of tablet, decreasing its wettability or by itself dissolved at a slower rate. 25 Matrix (or Monolith)/ Embedded dissolution controlled system. The dispersion of drug wax is prepared by dispersing the drug in the molten wax followed by congealing and granulating the same. The process, compression parameters and size of particles formed determine the release rate from this system. The drug release is often first order from such matrices. 26 Matrix (or Monolith)/ Embedded dissolution controlled system. 27 MARKETED FORMULATIONS Dosage form Nature of chemical entity Release mechanism Company Geomatrix Multilayered tablets - Dissolution Skye pharmaceuticals,p lc., (USA). Reduced irritation system Capsules - Dissolution DepoMed, Inc. Dimatrix (Diffusion consulted matrix system) Tablets - Dosage form Biovail corporation international, IDDAS (Intestinal Protective Drug Absorption) system Tablets Hydrophillic compounds Diffusion Elan corporation Multipor Tablets - Diffusion Ethical Holding,plc., (UK). PPDS (Pellatized Pulsatile Delivery Pellets (tablets) - Diffusion Andrx pharmaceuticals. 28 MARKETED FORMULATIONS SMHS (Solubility Modulating Hydrogel System) Tablets - Diffusion Andrx pharmaceuticals SPDS (Stablized Pellets Delivery System) Pellets Unstable drugs Diffusion Andrx pharmaceuticals RingCap Matrix tablets - Diffusion Alker MODAS (Multi Tablets porous oral drug absorption system) Tablets Diffusion and dissolution Elan corporation, (Ireland). PRODAS (Programmable Oral Drug Absorption System) Encapsulated minitablets Hydrophilic molecules Diffusion and Dissolution Elan corporation SODAS (Spheroidal Oral Drug Absorption System) Beads (capsules tablets) Diffusion and Dissolution Elan corporation. 29 EROSION CONTROLLED DRUG DELIVERY SYSTEM Erosion is defined as the disintegration of the polymer/ wax matrix, as a result of degradation and is characterized by material loss from the polymer generally in the physical state. Polymer or wax degradation or hydrolysis is brought by enzyme, pH change or due to osmotic pressure or hydrodynamic pressure that causes fragmentation. Erosion is effected by external stimuli, such systems can be classified under stimuli activated drug delivery system. 30 EROSION CONTROLLED DRUG DELIVERY SYSTEM It is classified on the type of stimuli: 1. Physical e.g. (osmotic pressure) 2. Chemical e.g.(pH) 3. Biological e.g. (enzyme) Examples of erodible matrices include hydrophobic materials ethyl cellulose and waxes. Depending on the erosion mechanism, polymer or waxes undergo either surface erosion or bulk erosion 31 EROSION CONTROLLED DRUG DELIVERY SYSTEM a) SURFACE EROSION: It occurs from the surface layers of the device only. It results in gradual decrease in the size of the device while the bulk phase remain un-degraded. There is a difference in erosion rate between the surface and centre of matrix, the process is also called as heterogeneous erosion. Surface erosion occurs when water penetration is restricted to device surface. 32 33 EROSION CONTROLLED DRUG DELIVERY SYSTEM b) BULK EROSION: it occurs throughout the polymer bulk and the process is thus called as homogenous erosion. Bulk erosion occurs when the water is readily able to penetrate the matrix of the device. 34 HYBRID SYSTEM IN DRUG DELIVERY They are also called as membrane cum matrix drug delivery system. These systems are those where the drug in matrix of releaseretarding material is further coated with a release controlling polymer membrane. It combines constant release kinetics of reservoir system with mechanical robustness of matrix system. 35 EROSION CONTROLLED DRUG DELIVERY SYSTEM Degradation by erosion normally takes place in devices that are prepared from soluble polymers. In such instances, the device erodes as water is absorbed into the systems causing the polymer chains to hydrate, swell, and ultimately dissolved away from the dosage form. Degradation can also result from chemical changes to the polymer including cleavage of covalent bonds, ionization and protonation either along the polymer backbone or on pendent side chains. 36 MATHEMATICAL MODELS There are various mathematical models 1) Zero order kinetics 2) First order kinetics 3) Weibull model 4) Higuchi model 5) Hixson Crowell model 6) Korsmeyer Peppas model 7) Baker- Lonsdale model 8) Hopfenberg model 37 38 ZERO ORDER KINETICS This model is used for dosage forms that do not disaggregate and release the drug slowly (assuming that area does not change and no equilibrium conditions are obtained). It can be represented by the following equation: Wo - Wt = Kt 39 Wo - Wt = Kt Where W is the initial amount of drug in the pharmaceutical dosage form, W is the amount of drug in the pharmaceutical dosage form at time t and K is a proportionality constant. Dividing this equation by W0 and simplifying. ft= kot Where ft = 1-(Wt –W0) and f represents the fraction of drug dissolved in time t and k0 the apparent dissolution rate constant or zero order release constant. 40 FIRST ORDER KINETICS This model is applied for dissolution studies, and also describe the absorption and elimination of some drugs. ln Qt = ln Q0 + Kt Qt = Drug amounts remaining to be released at time t Q0 = Drug amounts remaining to be released at zero hr Kt = First order release constant. A graph of drug release versus time will be linear. 41 WEIBULL MODEL A general empirical equation adopted by Weibull was used to describe the release process. Erodible matrix formulations follow this model. M = 1- e[-(t-Ti)b/a 42 HIGUCHI MODEL Diffusion matrix formulations follow this model. This model is used to study the release of water soluble and low soluble drugs incorporated in semisolid and / or solid matrixes. It is denoted by the following equation ft = KHt1/2 ft = fraction of drug released at time t KH = Higuchi release rate constant t = time 43 HIXSON – CROWELL MODEL Erodible matrix systems follow this model. When this model is used, it is assumed that release rate is limited by the drug particles dissolution rate, and not by the diffusion that may occur through polymeric matrix. It is represented by the following equation Wo1/3 – Wt1/3= Kst 44 HIXSON – CROWELL MODEL Wo1/3 – Wt1/3= Kst Where, Wo = initial amount of drug present in the matrix. Wt = amount of drug released in time t. Ks = release rate constant. 45 KORSMEYER- PEPPA’S MODEL Swellable polymer devices follow this model. This model is generally used to analyze the release of pharmaceutical polymeric dosage forms, when the release mechanism is not well known or when more than one type of release phenomena could be involved. It is denoted by the following equation. Mt/M∞ = Ktn 46 KORSMEYER- PEPPA’S MODEL Mt/M∞ = Ktn Where, Mt = amount released at time t M∞= amount released at infinite time K = release rate constant n = release exponents 47 BAKER- LANSDALE MODEL This model is suitable for microcapsules or microspheres. It describes the drug controlled release from a spherical matrix. ft = 3/2[1-(1-Mt/M∞)2/3] – Mt/M∞= Kt Where, Ft = fraction of drug released at time t Mt = amount released at time t M∞ = amount released at infinite time 48 HOPFENBERG MODEL This model was used for the release of drugs from surface- eroding devices with several geometries. This equation describes drug release from slabs, spheres and infinite cylinders displaying heterogeneous erosion. It is given by the following the equation. Mt/M∞ 1 – [1-k1t(t-l)]n 49 HOPFENBERG MODEL Mt = amount released at time t M∞ = amount released at infinite time K = rate constant Mt/M∞ 1 – [1-k1t(t-l)]n 50 OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL FORMULATION AND PROCESSING 51 CONTENTS CONCEPT OF OPTIMIZATION OPTIMIZATION PARAMETERS CLASSICAL OPTIMIZATION STATISTICAL DESIGN DESIGN OF EXPERIMENT OPTIMIZATION METHODS 52 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 53 INTRODUCTION 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. Optimization tech provide both depth of understanding & ability to explore & defend range for formulation & processing factors. 54 OPTIMIZATION PARAMETERS optimization parameters Problem types variable Constrained unconstrained dependent independent 55 VARIABLES Independent Formulating Variables Dependent processing Variables 56 VARIABLES Independent variables or primary variables : Formulations and process variables are directly under control of the formulator. These includes ingredients Dependent or secondary variables : These are the responses of the in progress material or the resulting drug delivery system. It is the result of independent variables 57 VARIABLES 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. 58 VARIABLES Response surface representing the relationship between the independent variables X1 and X2 and the dependent variable Y. 59 CLASSIC OPTIMIZATION It involves application of calculus to basic problem for maximum/minimum function. 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. 60 GRAPH REPRESENTING THE RELATION BETWEEN THE RESPONSE VARIABLE AND INDEPENDENT VARIABLE 61 CLASSIC OPTIMIZATION 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 62 STATISTICAL DESIGN These Techniques are divided in to two types. Experimentation continues as optimization proceeds It is represented by evolutionary operations(EVOP) and simplex methods. Experimentation is completed before optimization takes place. It is represented by classic mathematical & search methods. 63 STATISTICAL DESIGN There are two possible approaches Theoretical approach- If theoretical equation is known , no experimentation is necessary. Empirical or experimental approach – With single independent variable formulator experiments at several levels. 64 STATISTICAL DESIGN 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. 65 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% 66 TERMS USED 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 67 TERMS USED Optimization by means of an experimental design may be helpful in shortening the experimenting time. The design of experiments is a structured , organized 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 analyzed statistically. 68 TYPES OF EXPERIMENTAL DESIGN Completely randomized designs Randomized block designs Factorial designs Full Fractional Response surface designs Central composite designs Box-Behnken designs Adding centre points Three level full factorial designs 69 TYPES OF EXPERIMENTAL DESIGN Completely randomised Designs These experiments 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 factor, an important technique called blocking can be used to reduce or eliminate the contribution of these factors to experimental error. 70 FACTORIAL DESIGN Full: used for small set of factors Fractional: 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 71 FACTORIAL DESIGN 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. 72 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. 73 FACTORIAL DESIGN TAGUCHI: 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. 74 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 75 RESPONSE SURFACE DESIGNS 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 design. 76 RESPONSE SURFACE DESIGNS 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 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 designs-Star points take the value of +1 & -1 and cube points lie in the interior of the cube Faced –star points on the faces of the cube. 77 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. 78 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. 79 FACTORIAL DESIGN These are the designs of choice for simultaneous determination of the effects of several factors & their interactions. They are 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- for optimizing more number of factors 80 LEVELS OF FACTORS IN THIS FACTORIAL DESIGN FACTOR HIGH LEVEL(mg) LOWLEVEL(mg) A:stearate B:Drug C:starch 0.5 60.0 30.0 1.5 120.0 50.0 81 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 82 EXAMPLE OF FULL FACTORIAL EXPERIMENT Calculation of main effect of A (stearate) The main effect for factor A is 10-3 {-(1)+a-b+ab-c+ac-bc+abc]4 a + ab + ac + abc = = Main effect of A = _ (1) + b + c + bc 4 [487 + 426 + 456 + 522 – (475 + 421 + 525 + 472)] 4 10-3 0.022 cm 83 GENERAL OPTIMIZATION By 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 main effects. 84 FLOW CHART FOR OPTIMIZATION 85 APPLIED OPTIMIZATION METHODS Evolutionary operations Simplex method Lagrangian method Search method Canonical analysis 86 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 87 EVOLUTIONARY OPERATIONS (EVOP) 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 88 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 no. of factors. It is represented by triangle. It is determined by comparing the magnitude of the responses after each successive calculation 89 GRAPH REPRESENTING THE SIMPLEX MOVEMENTS TO THE OPTIMUM CONDITIONS 90 SIMPLEX METHOD 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) 91 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 92 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 93 STEPS INVOLVED (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 etc., 94 STEPS INVOLVED (EXAMPLE) 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 95 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%) 96 LAGRANGIAN METHOD 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 97 CONTOUR PLOT FOR TABLET HARDNESS 98 CONTOUR PLOT FOR TABLET DISSOLUTION(T50%) 99 GRAPH OBTAINED BY SUPER IMPOSITION OF TABLET HARDNESS & DISSOLUTION 100 CONTOUR PLOT FOR TABLET FRIABILITY 101 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 102 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 103 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 104 SEARCH METHOD 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. 105 TRANSLATION OF STATISTICAL DESIGN IN TO PHYSICAL UNITS Experimental conditions Factor X1= ca.phos/lactose -1.54eu -1 eu Base0 +1 eu +1.54eu 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 1.8 106 SEARCH METHOD 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 = a0+a1x1+…+a5x5+a11x12+…+a55x25+a12x1x2 +a13x1x3+a45 x4x5 107 SEARCH METHOD 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. 108 PLOT FOR A SINGLE VARIABLE 109 PLOT OF FIVE VARIABLES 110 PLOT OF FIVE VARIABLES 111 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. 112 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. 113 CANONICAL ANALYSIS 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 Y = Y0 +λ1W12 + λ2W22 +.. empherical response. 114 Thank you E-mail: [email protected] Cell No:00919742431000 115

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