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. HECKELPLOTS
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
kinetics with the interparticulate pores as the reactants and the
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
,
yields a linear graph having slope, k and intercept,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 particular value of Heckel plots arises from their ability to
identify the predominant form of deformation in a material.
• They have been used:
• (i) to distinguish between substances that consolidate by
fragmentation and those that consolidate by plastic deformation.
• (ii) as a means of assessing plasticity

5. • Materials that
deformation.
• Conversely, materials with higher mean yield
are comparatively soft readily undergo plastic
pressure values
usually undergo compression by fragmentation first, to provide 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=4F/ 𝜋 D2(P= applied pressure),F=compressional 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. Examples of Heckel plots

10. • 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

11. 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
.

12. • 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.
• Therefore, for certain formulation changes, establishing similarity
between dissolution profiles for the test and the
is considered
formulation batches in several media
justification.
reference
sufficient
• The assumption is that the test product is bioequivalent to the
reference product if in vitro similarity is established.

13. 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.

14. Similarity factors (f2)
1. For accepting product sameness under SUPAC-related changes.
2. To waive bioequivalence requirements for lower strengths of a
dosage form.
3. 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.

15. • 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.

16. Limits for similarity and dissimilarity factors
Difference factor Similarity factor Inference
0 100 Dissolution
profiles are
similar
≤ 15 ≥ 50 Similarly or
equivalence
of two profiles

17. Introduction to Higuchi 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.

18. ▶ 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.

19. 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.

21. Higuchi plot representation

22. Applications
Higuchi describes the drug release asa
diffusion process based on Fick’s law, square
root time dependent.
Thismodel isuseful forstudying the release of
water soluble and poorly soluble drugs from
variety of matrices, including solids and
semisolids.

23. Korsmeyer-Peppas Model
Introduction:
Korsmeyer et al (1983) derived a simple relationship
which described drug release from a polymeric system.
To find out the mechanism of drug release, first 60%drug
release data were fitted in peppas model

24. Processes involved in Peppas Model
▶ T here are several simultaneous processes considered in this
model:
▶ Diffusion of water into the tablet
▶ Swelling of the tablet as water enters
▶ Formation of gel
▶ Diffusion of drug and filler out of the tablet
▶ Dissolution of the polymer matrix

25. Key Attributes
▶ K ey attributes of the model include:
▶ Tablet geometry is cylindrical
▶ Water and drug diffusion coefficients vary as functions of water
concentration
▶ Polymer dissolution is incorporated
▶ Change in tablet volume is considered

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

27. ▶ 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

28. Assumptions based on model
▶ The following assumptions were made in this model:
▶ The generic equation is applicable for small values of tor short times and
the portion of release curve where Mt/M ∞ < 0.6should only be used to
determine the exponent n.
▶ Drug release occurs in a one dimensional way.
▶ The system’s length to thickness ratio should be at least 10.

29. 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.

30. 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.

31. 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.

32. 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

33. 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.

34. The Chi-Square Test for Goodness-of-Fit
• The chi-square test for goodness-of-fit uses frequency
data from a sample to test hypotheses about the shape or
proportions of a population.
• Each 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.

35. The Chi-Square Test for Goodness-of-Fit (contd)
• The 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.

36. 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:
1.Testing hypotheses about the relationship between two
variables in a population, or
2.Testing hypotheses about differences between proportions for two
or more populations.

37. ⦁ ANOV
A is the abbreviation for the full name of the method:
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.

39. 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.

40. ⦁ 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.

41. ⦁ 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)
⦁ The alternative hypothesis (H1) is that there is a
have different
between the means
weights
and groups.
in different
difference
(Walruses
months)

42. ⦁ 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)

43. 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.

44. ⦁ 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.

45. ⦁ 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.

46. ⦁ 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

47. ⦁ 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

48.  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-wayANOVA, the F-statistic is this ratio:
⦁ F = variation between sample means / variation within
the samples

49.  The technique of analysing variance in case of single
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

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

51.  This is particularly applicable to experiment otherwise
difficult to implement such as is the case in clinical trails.
 In the bioequivalence studies the similarities between the
samples will be analyzed withANOV
A only.
 Pharmacovigilance data can also be evaluated using
ANOVA.
 Pharmacodynamic data can also be evaluated with ANOV
A
only.
 That means we can analyze our drug is showing
pharmacological action or not’

52. THANK YOU!