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MODERN PHARMACEUTICS

• HECKEL PLOTS

• SIMILARITY FACTORS (F2)

• DISSIMILARITY FACTORS (F1)

BY : RAJESH KUMAR CHAUDHARY

M.PHARM (PHARMACEUTICS) I SEM

JAMIA HAMDARD UNIVERSITY

HECKEL PLOTS 2

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.

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• 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.

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• 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

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• Materials that are comparatively soft readily undergo plastic

deformation.

• Conversely, materials with higher mean yield 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.

Types of powders 6

• Hersey & Rees classified powders into three types A, B and 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 plastic deformation .

• Log 1/E =KyP+Kr

• Where , Ky is a material dependent constant(Ky = 1/3S, S=yield

strength)

• Kr = initial repacking stage

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• 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

Examples of Heckel plots 8

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• 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.

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• 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

Dissolution profile comparison 12

• 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

.

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• 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.

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• Therefore, for certain formulation changes, establishing similarity

between dissolution profiles for the test and the reference

formulation batches in several media is considered sufficient

justification.

• The assumption is that the test product is bioequivalent to the

reference product if in vitro similarity is established.

Dissimilarity factors (f1) 15

• 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.

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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.

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• 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.

• 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.

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• 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.

Limits for similarity and dissimilarity factors 19

Difference factor Similarity factor Inference

0 100 Dissolution profiles are

similar

≤ 15 ≥ 50 Similarly or equivalence

of two profiles

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