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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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