deepak.pptx

Overview on Study of consolidation parameters

1. STUDY OF CONSOLIDATION PARAMETERS

2. CONSOLIDATION An increase in the mechanical strength of the material resulting from particle or particle interaction. (Increasing in mechanical strength of the mass). Consolidation process (1) Cold welding: When the surface of two particles approach each other closely enough, (e.g. at separation of less than 50nm) their free surface energies result in strong attractive force, this process known as cold welding. (2) Fusion bonding: Contacts of particles at multiple points upon application of load, produces heat which causes fusion or melting. If this heat is not dissipated, the local rise in temperature could be sufficient to cause melting of the contact area of the particles.

3. HECK E L PLOTS Introduction: It is based upon analogous behavior to a first order reaction. Powder packing with increasing compression load is normally attributed to particle rearrangement, elastic and plastic deformation and particle fragmentation The Heckel analysis is a popular method of determining the volume reduction mechanism under the compression force Based on the assumption that powder compression follows first order kine t ics w i th t h e int e rpar t icul a te pore s as the re a ctants and t h e densification of the powder as the product Heckel plot allows for the interpretation of the mechanism of bonding.

4. In [1 / (1 - ρ R )] = k P + A Plotting the value of In [ 1 / (1 - ρ R )] against applied pressure, P, yie l ds a l i near graph having slope, k and int e rcept, A . The reciprocal of k yields a material-dependent constant known as yield pressure , P y which is inversely related to the ability of the material to deform plastically under pressure. Low values of Py indicate a faster onset of plastic deformation. This analysis has been extensively applied to pharmaceutical powders for both single and multicomponent systems. The par t icu l ar v a lue of Heckel p l o ts arises from the i r a b i lity to identify the predominant form of deformation in a material. They have been used: (i ) t o dis t ingu i sh b etween s u bst a n ces t h at cons o l i date by fragmentation and those that consolidate by plastic deformation. (ii) as a means of assessing plasticity

5. M a terials t h at deformation. C o nversel y , m ateri a ls with h igh e r m e a n yi el d a re c o m parativ e ly soft re a d i ly unde r go plastic pressure values us ual l y unde r go co m pre ss ion by frag m enta t ion firs t, t o p rovide a denser packing. Hard, brittle materials are generally more difficult to compress than soft ones.

6. Types of powders Hersey & Rees classified powders into three types A, Band C . The classification is based on Heckel plots and the compaction behavior of the material . With type A materials, a linear relationship is observed, with the plots remaining parallel as the applied pressure is increased indicating deformation apparently only by plasticde formation . Log1/E= KyP+Kr Where, Ky is a material dependent constant ( Ky =1/3S,S=yield strength ) Kr=initial repacking stage

7. P=4 F / 𝜋 D2 (P= ap p l i ed pressu r e) , F=co m pre ss ion a l force, D=diameter of tablet E=100[1-4w/ρtπD2 H] w = weight of tablet, E= porosity of powders ρt = true density H=thickness of tablet Curves i,ii,iii represent decreasing particle size fraction of the same material Type a curves are typical of plastically deforming materials Type b curves shows initially fragmentation

8. Example s o f H e ckel plots

9. An example of materials that exhibit type A behavior is sodium chloride. Type A materials are usually comparatively soft and readily undergo plastic deformation retaining different degrees of porosity depending on the initial packing of the powder in the die. This is in turn influenced by the size distribution, shape, e.t.c., of the original particles. Type B Heckel plots usually occur with harder materials with higher yield pressures which usually undergo compression by fragmentation first, to provide a denser packing. Lactose is a typical example of such materials. For type C materials, there is an initial steep linear region which become superimposed and flatten out as the applied pressure is increased e.g. starch

10. Dissolution profile comparison The dissolution profile comparison may be carried out using model independent or model dependent methods Extensive applications throughout the product development process. When composition, manufacturing site, scale of manufacture, manufacturing process and/or equipment have changed within defined limits, dissolution profile comparison can be used to establish the similarity between the formulations A dissolution profile comparison between pre-change and post- change products for SUPAC related changes, or with different strengths, helps assure similarity in product performance and signals bioinequivalence .

11. The FDA has issued guidance documents for both immediate-release (IR) formulations and modified-release (MR) formulations . These documents indicate the type of data that are accepted in support of post-approval changes to the formulation, aim is to reduce the regulatory burden by decreasing both the number of manufacturing changes that require FDA prior approval and the number of bioequivalence studies necessary to support these changes. The r efor e , for c ert a in f or m ulation change s , e s tab l ishing s i m i l ar i ty be t wee n d i sso lu t ion p rofiles for the te s t and the is considered fo r m ul a t i on batc h es i n several m edia justification. referen c e su f f icie n t The assu m p tion i s that the test p roduct i s b i o equiv a lent t o t h e reference product if in vitro similarity is established.

12. Dissimilarity factors (f1) The difference factor (f1) calculates the percent (%) difference between the two curves at each time point and is a measurement of the relative error between the two curves: f 1 = {[Σ t=1 to n| Rt - T t| ]/[Σt=1 to n Rt ]}* 100 where n is the number of time points, Rt is the dissolution value of the reference (prechange) batch at time t, and Tt is the dissolution value of the test (postchange) batch at time t.

13. Similarity factors (f2) For accepting product sameness under SUPAC-related changes. To waive bioequivalence requirements for lower strengths of a dosage form. To support waivers for other bioequivalence requirements. The similarity factor (f2 ) is a logarithmic reciprocal square root transformation of the sum of squared error and is a measurement of the similarity in the percent (%) dissolution between the two curves. f2 = 50 * log {[1+(1/n)Σt=1 to n ( Rt - Tt )2 ]-0.5 }* 100 where Log=logarithm to base 10, n=number of sampling time points, ∑=summation over all time points, Rt and Tt are the reference and test dissolution values (mean of at least 12 dosage units) at time point t. The value of f2 is 100 when the test and reference mean profiles are identical .

14. A specific procedure to determine difference and similarity factors is as follows: 1. Determine the dissolution profile of two products (12 units each) of the test ( postchange ) and reference ( prechange ) products. 2. Using the mean dissolution values from both curves at each time interval, calculate the difference factor (f1 ) and similarity factor (f2 ) using the above equations. 3. For curves to be considered similar, f1values should be close to 0, and f2 values should be close to 100. Generally, f1 values up to 15 (0-15) and f2 values greater than 50 (50-100) ensure sameness or equivalence of the two curves and, thus, of the performance of the test (postchange) and reference (prechange) products.

15. Limits for similarity and dissimilarity factors Difference factor Similarity factor Inference 100 D i ss o l u t i on pr o f i l e s a re similar ≤ 15 ≥ 50 S i m i l a rly or e q u iv a l en ce of two profiles

16. Introductio n to Hi g uchi plot ▶ Ideally, controlled drug-delivery systems should deliver the drug at a controlled rate over a desired duration. ▶ The primary objectives of the controlled drug-delivery systems are to ensure safety and to improve efficacy of drugs, as well as to improve patient compliance. ▶ Of the approaches known for obtaining controlled drug release, hydrophilic matrix is recognized as the simplest and is the most widely used. Hydrophilic matrix tablets swell upon ingestion, and a gel layer forms on the tablet surface. This gel layer retards further ingress of fluid and subsequent drug release.

17. ▶ It has been shown that in the case of hydrophilic matrices, swelling and erosion of the polymer occurs simultaneously, and both of them contribute to the overall drug-release rate. ▶ It is well documented that drug release from hydrophilic matrices shows a typical time-dependent profile (ie, decreased drug release with time because of increased diffusion path length). This leads to first-order release kinetics. ▶ In 1961, Higuchi tried to relate the drug release rate to the physical constants based on simple laws of diffusion. ▶ Higuchi was the first to derive an equation to describe the release of a drug from an insoluble matrix as the square root of a time-dependent process based on Fickian diffusion .

18. Higuchi’s hypothesis includes ▶ Initial drug concentration in the matrix is much higher than drug solubility. ▶ Drug diffusion takes place only in one dimension. ▶ Drug particles are much smaller than system thickness. ▶ Matrix swelling and dissolution are negligible. ▶ Drug diffusivity is constant. ▶ Perfect sink conditions are always attained in the release environment.

19. Higuch i plo t representation

20. Applications H i guchi descr i be s the dru g rel e as e a s a diffusion process based on Fick’s law, square ro o t t i me dependent. Th i s m o de l i s usef u l f o r study i n g the re l e a s e o f water soluble and poorly soluble drugs from variety of matrices, including solids and semisolids.

21. Ko r smeyer - Pep p a s Model Introduction: Korsmeyer et al (1983) derived a simple relationship wh i ch descr i be d drug relea s e from a polymer i c sys t em. To find out the mechanism of drug release, first 60%drug release data were fitted in peppas model

22. Processes involved in Peppas Model ▶ T her e a r e s e v er a l s i mult a n eou s processe s cons i dere d i n t h i s model: ▶ Diffusion of water into the tablet ▶ Swelling of the tablet as water enters ▶ F o r mat i on of g el ▶ Diffusion of drug and filler out of the tablet ▶ D i ssolution of the po l ym e r matr i x

23. Key Attributes ▶ K e y a tt r i b u t e s o f t h e mode l i nclud e : ▶ T able t g eomet r y is cylindr i cal ▶ Water and drug diffusion coefficients vary as functions of water concentration ▶ Polymer dissolution is incorporated ▶ Change in tablet volume is considered

24. KORSEMEYAR AND PE P PAS EQUATION ▶ The KORSEMEYAR AND PEPPAS empirical expression relates the function of time for diffusion controlled mechanism. ▶ It is given by the equation : M t / M a = Kt n where, ▶ Mt / Ma is fraction of drug released ▶ t = time ▶ K=constant includes structural and geometrical characteristics of the dosage form

25. ▶ n= release component which is indicative of drug release mechanism where , n is diffusion exponent. ▶ i. If n= 1 , the release is zero order ▶ ii. n = 0.5 the release is best described by the Fickian diffusion ▶ iii. 0.5 < n < 1 then release is through Anomalous diffusion 19

26. Ass u mptions base d o n model ▶ The following assumptions were made in this model: ▶ The generic equation is applicable for small values of t or short times and the portion of release curve where M t /M ∞ < 0.6 should only be used to determine the exponent n. ▶ D r ug release oc c urs in a one d i me n sional w a y . ▶ The sy s tem ’ s length to thi c kn e ss ra t io sho u ld be at least 10.

27. Peppas Plot To study the release kinetics, data obtained from in vitro drug release studies were plotted as log cumulative percentage drug release versus log time.

28. Applications ▶ This model has been used frequently to describe the drug release from several modified release dosage forms. ▶ This equation has been used to the linearization of release data from several formulations of microcapsules or microspheres ▶ Use to analyze the release of pharmaceutical polymeric dosage form. ▶ When the release mechanism is not known or when more than one type of release phenomena could be involved.

29. Chi Square Test Two non-parametric hypothesis tests using the chi-square statistic: the chi-square test for goodness of fit and the chi-square test for independence.

30. Relation of Chi square test to parametric and non parametric tests • The term "non-parametric" refers to the fact that the chi-square tests do not require assumptions about population parameters nor do they test hypotheses about population parameters. • previous examples of hypothesis tests, such as the t tests and analysis of variance, are parametric tests and they do include assumptions about parameters and hypotheses about parameters

31. Relation of Chi square test to parametric and non parametric tests ( Contd ) • The difference between the chi-square tests and the other hypothesis tests we have considered (t and anova ) is the nature of the data. • for chi-square, the data are frequencies rather than numerical scores.

32. The Chi-Square Test for Goodness-of-Fit • T he chi-square test for goodness-of-fit uses frequency data from a sample to test hypotheses about the shape or proportions of a population. • E ach individual in the sample is classified into one category on the scale of measurement. • the data, called observed frequencies , simply count how many individuals from the sample are in each category.

33. The Chi-Square Test for Goodness-of-Fit ( contd ) • T he null hypothesis specifies the proportion of the population that should be in each category. • the proportions from the null hypothesis are used to compute expected frequencies that describe how the sample would appear if it were in perfect agreement with the null hypothesis.

34. The Chi-Square Test for Independence ▶ The second chi-square test, the chi-square test for independence , can be used and interpreted in two different ways: Testing hypotheses about the relationship between two variables in a population, or Testing hypotheses about differences between proportions for two or more populations.

35. ANO V A i s the abb r evi a tion for the full na m e of the m etho d : Analysis of variance. Invented by Ronald Fischer. Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample. Example: A group of psychiatric patients are trying three different therapies: counseling, medication and biofeedback. You want to see if one therapy is better than the others.

36. A one way ANOVA is used to compare two means from two independent (unrelated) groups using the F-distribution. When to use a one way ANOVA Situation : You have a group of individuals randomly split into smaller groups and completing different tasks. For example, you might be studying the effects of tea on weight loss and form three groups: green tea, black tea, and no tea.

37. Here, the independent variable or factor (the two terms mean the same thing) is “month of mating season”. In an ANOVA, our independent variables are organised in categorical groups. For example, if the researchers looked at walrus weight in December, January, February and March, there would be four months analyzed, and therefore four groups to the analysis.

38. In a one-way ANOVA there are two possible hypotheses. The null hypothesis (H0) is that there is no difference between the groups and equality between means. (Walruses weigh the same in different months) Th e alt e r native hyp o thesi s ( H 1 ) is t h a t t h er e i s a have different between the means w e ights and gro u p s. i n dif f e r ent d iff ere n ce (Walruses months)

39. Normality – That each sample is taken from a normally distributed population Sample independence – that each sample has been drawn independently of the other samples Variance Equality – That the variance of data in the different groups should be the same Your dependent variable – here, “weight”, should be continuous – that is, measured on a scale which can be subdivided using increments (i.e. grams, milligrams)

40. A one way ANOVA will tell you that at least two groups were different from each other. But it won’t tell you what groups were different.

41. A two-way ANOVA is, like a one-way ANOVA, a hypothesis-based test. It examines the influence of two different categorical independent variables on one continuous dependent variable. The two-way ANOVA not only aims at assessing the main effect of each independent variable but also if there is any interaction between them.

42. Your dependent variable – here, “weight”, should be continuous – that is, measured on a scale which can be subdivided using increments (i.e. grams, milligrams) Your two independent variables – here, “month” and “gender”, should be in categorical, independent groups.

43. Sample independence – that each sample has been drawn independently of the other samples Variance Equality – That the variance of data in the different groups should be the same Normality – That each sample is taken from a normally distributed population

44. There are three pairs of null or alternative hypotheses for the two-way ANOVA. Here, for walrus experiment, where month of mating season and gender are the two independent variables. H0: The means of all month groups are equal H1: The mean of at least one month group is different H0: The means of the gender groups are equal H1: The means of the gender groups are different H0: There is no interaction between the month and gender H1: There is interaction between the month and gender

45. The F-test can assess the equality of variances. F-tests are named after its test statistic, F, which was named in honor of Sir Ronald Fisher. The F-statistic is simply a ratio of two variances. Variance is the square of the standard deviation. To use the F-test to determine whether group means are equal, it’s just a matter of including the correct variances in the ratio. In one-way ANOVA, the F-statistic is this ratio: F = variation between sample means / variation within the samples

46. The t e c h ni q ue o f a n a lysing vari a nce i n c a se o f s i n g l e variable and in case of two variable is similar. In both cases a comparision is made between the variance of sample means with the residual variance. However, in case of single variable, the total variance is divided into two two parts only,viz.., Variance between the samples and the variance within the samples

47. The later variance is the residual variance. In case of two variables the total variance is divided in three parts viz.., Variance due to variable no.1 Variance due to variable no.2 Residual variance

48. Th i s i s p a rtic u la r ly a pp l icab l e t o experi m ent ot h erwise difficult to implement such as is the case in clinical trails. I n t h e bi oe quiva l ence studies the si m ilari t ies be t wee n t h e s a m p l es will be ana l yzed with A N O V A onl y . Pharmacovigilance data c an a lso be ev a lua t ed using ANOVA. Pha r m a c odyna m ic data can a lso be eva l u a ted with AN O V A only. That m eans w e can an a lyze our drug i s show i ng pharmacological action or not’

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