HECKEL PLOT CEUTICS .pptx

NARGUND COLLEGE OF PHARMACY

1. Heckal plots, similarity factor f1 and f2, Higuchi and krosmeyer-peppas model, linearity concept of significance, standard deviation, chi-square test, student-t test, anova test Presented by: ABDUL NAIM M pharm 1 st year Dept of pharmaceutics Nargund college of pharmacy

2. SIMILARITY FACTORS F1AND F2: DIFFERENCE FACTOR (f1): The difference factor (f1) as defined by FDA calculates the % difference between 2 curves at each time point and is a measurement of the relative error between 2 curves. Where, n = number of time points Rt = % dissolved at time t of reference product(pre change) Tt = % dissolved at time t of test product (post change). SIMILARITY FACTOR (f2): The similarity factor (f2) as defined by FDA is logarithmic reciprocal square root transformation of sum of squared error and is a measurement of the similarity in the percentage (%) dissolution between the two curves.

3. Difference factor Similarity factor Inference 100 Dissolution profile are similar < 15 > 50 Similarity or equivalence of two profiles Limits for similarity factor and difference factor: Data structure and steps to follow: • This model-independent method is most suitable for the dissolution profile comparison when three to four or more dissolution time points are available. • Determine the dissolution profile of two products (12 units each) of the test (post change) and reference (pre-change) products.

4. • 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. • For curves to be considered similar, f1 values 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 (post-change) and reference (pre-change) products. • In dissolution profile comparisons, especially to assure similarity in product performance, the regulatory interest is in knowing how similar the two curves are, and to have a measure which is more sensitive to large differences at any particular. Some recommendations: The dissolution measurements of the test and reference batches should be made under exactly the same conditions.

5. • The dissolution time points for both the profiles should be the same (e.g. 15, 30, 45, 60 minutes). • The reference batch used should be the most recently manufactured pre-change product. • Only one measurement should be considered after 85% dissolution of both the products (when applicable). • To allow use of mean data, the percent coefficient of variation (% CV) at the earlier time points (e.g. 15 minutes) should not be more than 20%, and at other time points should not be more than 10%. • The mean dissolution values for reference can be derived either from last pre-change batch or the last two or more consecutively manufactured pre-change batches Applications: • This method is more appropriate when more than three or four dissolution time points are available.

6. • The f2 may become invariant with respect to the location change and the consequence of failure to take into account the shape of the curve and the unequal spacing between sampling time points lead to errors. • Nevertheless, with a slight modification in the statistical analysis, similarity factor would definitely serves as an efficient tool for reliable comparison of dissolution profiles. Advantages: 1. They are easy to compute. 2. They provide a single number to describe the comparison of dissolution profile data. Disadvantages: 1. The values of f1 and f2 are sensitive to the number of dissolution time points used. 2. The basis of the criteria for deciding the difference or similarity between dissolution profile is unclear

7. HECKEL PLOT: • The Heckel analysis is a most popular method of deforming reduction under compression pressure . • Powder packing with increasing compression load is normally attributed to particles rearrangement , elastic & plastic deformation & particle fragmentation. • It is analogous to first order reaction ,where the pores in the mass are the reactant , that is: Log 1/E= Ky . P + Kr Where….. Ky =material dependent constant inversely proportional to its yield strength ‘s’ Kr=initial repacking stage hence E0 The applied compressional force F & the movement of the punches during compression cycle & applied pressure P , porosity E. • For a cylindrical tablets p=4F/л. D2 Where… D is the tablet diameter similarly E can be calculated by E=100.(1-4w/ ρt .л.D2.H)

8. Where…w is the weight of the tableting mass , ρt is its true density , H is the thickness of the tablets. • Heckel plot is density v/s applied pressure • Follows first order kinetics • As porosity increases compression force also increases • Thus the Heckel’s plot allows for the interpretation of the mechanism of bonding. • Materials that are comparatively soft & that readily undergo plastic deformation retain different degree of porosity , depending upon the initial packing in the die. • Harder material with higher yield pressure values usually undergo compression by fragmentation first, to provide a denser packing. EX: Lactose, sucrose (shown in type b in graph)

9. Compressional force Log E -1 Log E-1 Heckel plots: (a) material undergoing plastic deformation; (b) material undergoing brittle fracture APPLICATION OF HECKEL EQUATION: • Heckel plots can be influenced by the overall time of compression, the degree of lubrication and even the size of the die, so that the effects of these variables are also important and should be taken into consideration. • Larger k values usually indicate harder tablets. • Such information can be used as a means of binder selection when designing tablet formulations .

10. • The crushing strength of tablets can be correlated with the values of k of the Heckel plot. HIGUCHI MODEL: The first example of a mathematical model aimed to describe drug release from a matrix system was proposed by Higuchi in 1961. This model is based on the hypothesis that ( i ) drug diffusion takes place only in one dimension (ii) drug particles are much smaller than system thickness (iii) drug diffusivity is constant (iv) perfect sink conditions are always attained in the release environment. Accordingly, model expression is given by the equation: ft = Q = A √D(2C ñ Cs) Cs t where Q is the amount of drug released in time t per unit area A, C is the drug initial concentration, Cs is the drug solubility in the matrix media and D is the diffusivity of the drug molecules (diffusion coefficient) in the matrix substance.

11. Initial drug concentration in matrix is much higher. As drug is released distance for diffusion is progressively increases. Drug is leached out polymer matrix by entrance of surrounding medium. In release environment perfect sink is maintained . Higuchi equation model: The Equation Of Higuchi model: Q =[D(2A-C s )Cs×t] 1/2 OR Q=(2ADCst) 1/2 By differentiating above equation we get, dQ/dt=(ADCs/2t) 1/2

12. The Drug release from granular matrix is given by: Where, dQ / dt - rate of drug release Cs- Solubility of drug in matrix A- Total Concentration of drug in matrix D- Diffusion Coefficient t- Time €- porosity of matrix t- Tortuosity

13. The data obtained were plotted as cumulative percentage drug release versus square root of time. Application: This relationship can be used to describe the drug dissolution from several types of modified release pharmaceutical dosage forms, as in the case of some transdermal systems and matrix tablets with water soluble drug.

14. KORSMEYER-PEPPAS MODEL: 1. Korsmeyer et al. (1983) derived a simple relationship which described drug release from a polymeric system equation. 2.To find out the mechanism of drug release, first 60% drug release data were fitted in Korsmeyer Peppas mode . F = Mt / M∞ = K m t n Where, Mt / M∞ is a fraction of drug released at time t k is the release rate constant and n is the release exponent. The n value is used to characterize different release for cylindrical shaped matrices.

15. To find out the exponent of n the portion of the release curve, where Mt / M∞ <0.6 should only be used. • To study the release kinetics, data obtained from in vitro drug release studies were plotted as log cumulative percentage drug release versus log time .

16. Linearity concept of significance: Definition of significance Testing : In statistics, it is important to know if the result of an experiment is significant enough or not. In order to measure the significance, there are some predefined tests which could be applied. These tests are called the tests of significance or simply the significance tests. • This statistical testing is subjected to some degree of error. For some experiments, the researcher is required to define the probability of sampling error in advance. In any test which does not consider the entire population, the sampling error does exist. The testing of significance is very important in statistical research. • The significance level is the level at which it can be accepted if a given event is statistically significant. This is also termed as p-value. • It is observed that the bigger samples are less prone to chance, thus the sample size plays a vital role in measuring the statistical significance. One should use only representative and random samples for significance testing.

17. • In short, the significance is the probability that a relationship exists. Significance tests tell us about the probability that if a relationship we found is due to random chance or not and to which level. This indicates about the error that would be made by us if the found relationship is assumed to exist. Objectives of linearity testing : The statistical significance refers to the probability of a result of some statistical test or research occurring by chance. • The main purpose of performing statistical research is basically to find the truth. • In this process, the researcher has to make sure about the quality of sample, accuracy, and good measures which need a number of steps to be done. • The researcher has to determine whether the findings of experiments have occurred due to a good study or just by fluke.

18. Process of Significance Testing : In the process of testing for statistical significance, there are the following steps: 1. Stating a Hypothesis for Research 2. Stating a Null Hypothesis 3. Selecting a Probability of Error Level 4. Selecting and Computing a Statistical Significance Test 5. Interpreting the results The claim tested by a statistical test is called the null hypothesis (H0). The test is designed to assess the strength of the evidence against the null hypothesis. Often the null hypothesis is a statement of “no difference.” The claim about the population that evidence is being sought for is the alternative hypothesis (Ha).

19. ➢ When using logical reasoning, it is much easier to demonstrate that a statement is false, than to demonstrate that it is true. This is because proving something false only requires one counter example. ➢ Proving something true, however, requires proving the statement is true in every possible situation. ➢ For this reason, when conducting a test of significance, a null hypothesis is used. ➢ The term null is used because this hypothesis assumes that there is no difference between the two means or that the recorded difference is not significant. ➢ The notation that is typically used for the null hypothesis is H0. ➢ The opposite of a null hypothesis is called the alternative hypothesis. ➢ The alternative hypothesis is the claim that researchers are actually trying to prove is true. However, they prove it is true by proving that the null hypothesis is false. ➢ If the null hypothesis is false, then its opposite, the alternative hypothesis, must be true. The notation that is typically used for the alternative hypothesis is Ha.

20. Standard deviation: Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. ✓ The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set. Like the variance, if the data points are close to mean, there is a small variation whereas the data points are highely spread out form the mean, then it has a high variance. ✓ Standard deviation is denoted by the symbol σ, describes the square root of the mean of the squares of all the values of a series derived from the arithmetic mean which is also called as the root-mean-square deviation. ✓ 0 is the smallest value of standard deviation since it cannot be negative. When the elements in a series are more isolated from the mean, then the standard deviation is also large

21. Formula for standard deviation : Where, ∑ sum means "sum of", x is a value in the data set, x bar is the mean of the data set, n is the number of data points in the population

22. Merits of Standard Deviation: 1- It is the most reliable measure of dispersion 2- It is most widely used measure of dispersion or variability 3- Its computation is based on all the observations Demerits of Standard Deviation: 1- It is relatively difficult to calculate and understand. 2- It cannot be used for comparing the dispersion of two, or more series given in different units. 3- It is affected very much by the extreme values

23. Summary: Standard deviation measure the dispersion of data. It is the most reliable The greater the value of standard deviation, the further the data tend to be dispersed from the mean.

24. Chi-Square test: A chi-squared test (symbolically represented as χ2) is basically a data analysis on the basis of observations of a random set of variables. Usually, it is a comparison of two statistical data sets. • This test was introduced by Karl Pearson in 1900 for categorical data analysis and distribution. • So it was mentioned as Pearson’s chi-squared test. • A chi-square statistic is one way to show a relationship between two categorical variables. • In statistics, there are two types of variables: numerical (countable) variables and non-numerical (categorical) variables • The chi-squared statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population

25. Properties chi-squared test: 1. Two times the number of degrees of freedom is equal to the variance. 2. The number of degree of freedom is equal to the mean distribution 3. The chi-square distribution curve approaches the normal distribution when the degree of freedom increases. Formula; Or χ2 = ∑(Oi – Ei )2/ Ei Where, Oi is the observed value Ei is the expected value

26. Student’s t-test: • T Distribution also called the student’s t-distribution and is used while making assumptions about a mean when we don’t know the standard deviation. • In probability and statistics, the normal distribution is a bell-shaped distribution whose mean is μ and the standard deviation is σ. • There are two Student’s t-tests; one evaluates pairs of results with something in common, known as the dependent test, tdep . The other compares the averages of independent results, tind .

27. T Distribution Formula: In this equation, x̄ is the sample mean μ is the population mean, s is the sample standard deviation, and n is the number of observations in the sample. example of a dependent design is comparing the results obtained from the same individuals before and after a treatment. • An independent design would be, for instance, comparing the resultsobtained in groups of healthy men and women. • Thus, the tdep considers the difference between every pair of values, whereas the tind only considers the averages, the standard deviation and number of observations in each group. Access to these intermediary quantities allows calculating the tvalue .

28. Properties of T Distribution : 1. It ranges from −∞ to +∞. 2. It has a bell-shaped curve and symmetry similar to normal distribution. 3. The shape of the t-distribution varies with the change in degrees of freedom. 4. The variance of the t-distribution is always greater than ‘1’ and is limited only to 3 or more degrees of freedom. It means this distribution has a higher dispersion than the standard normal distribution.

29. ANOVA test: If a specific quantity of a given sample is measured repeatedly on several occasions, e.g. using different instruments or on different days, it may be interesting to compare the averages in the groups or from the various occasions. The procedure of choice in this case is the ANOVA. The ANOVA reduces the risk of overestimating a significance of differences caused by chance which may be an effect of repeated tind . ✓ It also shows us a way to make multiple comparisons of several populations means. ✓ The Anova test is performed by comparing two types of variation, the variation between the sample means, as well as the variation within each of the samples.

30. Types of ANOVA : One Way ANOVA – It is also known as one factor ANOVA. Here, we are using one criterion variable (or called as a factor) and analyze the difference between more than two sample groups. Suppose in glass industry, we want to compare the variation of three batches (glass) for their average weight (factor).

31. Example : From Table 1, 20 patient’s DBP (at 30 min) are given. One‑way ANOVA test was used to compare the mean DBP in three age groups (independent variable), which was found statistically significant (p = 0.002). Levene test for homogeneity was insignificant (p = 0.231), as a result Bonferroni test was used for multiple comparisons, which showed that DBP was significantly different between two pairs i.e., age group of <30 to 30–50 and <30 to >50 (P < 0.05) but insignificant between one pair i.e., 30–50 to >50 (P > 0.05)

32. 2. Two Way ANOVA – Here, we are using two independent variables (factors) and analyze the difference between more than two sample groups. Similarly, we want to compare the variation of three batches of glass weight and hardness (two factors). Example : From Table 1, 20 patient’s DBP (at 30 min) are given. Two‑way ANOVA test was used to compare the mean DBP between age groups (independent variable_1) and gender (independent variable_2), which indicated that there was no significant interaction of DBP with age groups and gender (tests of Between‑Subjects effects in age groups*gender; P = 0.626) with effect size (Partial Eta Squared) of 0.065. The result also showed that there was significant difference in estimated marginal means (adjusted mean) of DBP between age groups (P = 0.005) but insignificant in gender (P = 0.662), where sex and age groups was adjusted